swansont

Not sure why, but my brain completely skipped over that bit when I was reading.

Nobody has claimed this to be true.

It's how they are defined. If you had point with a finite length, you can make a point that's half the size. If you have endpoints a fine distance apart, you can choose a point between them. Keep doing so. The limiting case is that points have zero length. You aren't counting points when you do this.

Why not? How much information is in the natural numbers? You need to rigorously quantify these things, rather than assert them. There are lots of infinities in physics, but they are described by math How many solutions are there for the principle quantum number for the Hydrogen atom (Schrödinger or Bohr solution; pick whichever one you want)

I would think loss of arctic ice would be a significant contribution, since the water reflects less well than the ice. And, of course, light not reflected is being absorbed, contributing to heating.

But that doesn't limit the math. You seem to be insisting that it does. Your thread title is all about math and nothing about physical things.

Some kind of epoxy or resin might achieve this. Soft (possibly liquid) until it’s cured. Probably ends up harder than sealing wax

Numbers don’t physically exist. But these aren’t the same thing. A volume of spacetime is not the same as the points inside it.

! Moderator Note Is a digital signature sticky? Can you prepare a small amount for obtaining a relief pattern to yield a negative? No? Then this is off-topic.

It's settled math. You can pick any two points and always find a point in between them. But not an infinite amount of time. Math is a labor-saving device. Otherwise this doesn't seem to be pertinent. Again, not pertinent to the OP.

What does this have to do with anything? You mentioned points in space, not time. I specified a line segment in space, and noted that there are an infinite number of points in it. No mention of time at all. None. Space is not impacted by gravity. The curvature of space is gravity. A little more specifically, mass (really, energy-momentum) causes space to curve, which we perceive as gravity. Yes. Because if the photon had mass then it wouldn't behave the way it does. Note that this is physics and not philosophy, and seems to be OT for this thread. There have been other discussions about this, and you are free to start a new one (in an appropriate subforum) if you actually want to discuss the physics of it.

I'd be worried about the craft tipping over in the high winds you'd be seeking out. I would expect that would limit the size of the impeller you could safely deploy. Also the cost/benefit ratio of something that you'd be deploying perhaps a dozen trips a year vs just harnessing the normally-encountered winds on a fixed platform.

It's called sealing wax. Available in craft stores and on the web. I think some of the bottling material is not actually wax, or there are additives to it.

! Moderator Note Which can and will be ignored on this, a science discussion site, as a response to any inquiry having to do with mainstream topics.

No, the line is not time. You said space, and I meant space. There are an infinite number of points in any volume of space. You previously said points, not planck lengths. A point has no length. Don’t change the argument

You have an infinite number of points in any finite, one-dimensional line segment. So this is incorrect. Infinities are useful in analysis We absolutely count finite things.

Sorry, I missed the r=1 detail…but you are assuming a one-dimensional system, which is a special case. The speed distribution arises from having a 3-D system. Collisions don’t have to be head-on. Both particles will be moving after the collision, except for the head-on case.

No. If one particle is at rest, both particles will be moving after the collision.

You haven’t shown that this is true. Not even close.

Noted. But you are insisting that you have to change G, because of this hand-wavy argument, rather than trying to find out the correct transform.

You seem to be assuming that the values will have to agree with each other, when we know that instead, such values are relative and can only be compared by transforming from one reference frame into the other. I don't know off the top of my head what value a distant observer would calculate for g in a GR context. What I do know is if this were a situation where relative motion were in play, they would not get the same answer for an acceleration, because that's not how accelerations transform, just like they would not get the same answer for kinetic energy of some object in the other frame, and whose value is not found by a simple multiplication by gamma. Relative values will be relative, not equal, in different frames of reference. Are you arguing that g is an invariant quantity? because that's what you seem to be arguing.

We already know that there's a large chunk of the electorate in many countries that do not value this trait.

And a whole host of other politicians. Defining characteristics of authoritarian leaders includes the appeal to emotion and not fact. I don't think they would be in favor of science beyond what they could pervert to align with and achieve their goals. And they preach hatred and division rather than unity Even really horrible people are going to have some things in common with good. Focusing on the commonalities does nothing to distinguish them.

Yes, this is basically the problem, along with his clarification "By the phrase "exotic matter" I mean matter that has negative energy and therefore anti-gravitates, i.e. repels." First of all, the Casimir force is attractive, not repulsive. The plates get pushed together. It also has nothing to do with gravity - the derivation of the force relies on the electric and magnetic field boundary conditions applied to the conducting plates; it's purely an electromagnetic phenomenon. You eliminate photon standing wave modes (of one polarization) because the field needs to go to zero at the boundary. The QM solution says for the vacuum, each state has an energy of hv, so there are fewer photon modes inside the plates than outside. The energy density imbalance means there is a pressure that pushes them together. In short, if the plates are a micron apart, then no photon states of 2 microns or longer can exist in between the plates (plus more that wouldn't form standing waves) but they do exist outside the plates. There's no gravity involved, and no matter identified with it, AFAICT. Maybe his point is that if the Casimir force exists maybe there's something like this for gravity, but still, the Casimir force isn't tied to exotic matter and it's attractive and it relies on there being boundary conditions for E and B fields that AFAIK don't exist for gravity, so it would be a really weak analogue for the kind of exotic matter you need for wormholes to become stable

I think this overview is very handwavy*, but seeing as there are some examples given, I'd like to see how one would get to relativity from having a cosmic speed limit (i.e. limiting c but not making it invariant), and without the components that Einstein used to get to Lorenz-Fitzgerald contraction. How would one eliminate the wrong explanations? Seems like they admit this isn't what's actually happening. You can't have a mother of all theories if that mother isn't giving birth to the theories, and they basically admit that's not what is (or would be) happening. This seems more like a big-picture view where you can make sense of some concepts you didn't necessarily know were related. Something like understanding that continuous symmetries give rise to conservation laws. *I can't tell who is overselling this more, the scientists or the person who wrote the article